College Algebra 7th Edition

by
Stewart, James; Redlin, Lothar; Watson, Saleem

Published by
Brooks Cole

ISBN 10:
1305115546

ISBN 13:
978-1-30511-554-5

Chapter 2, Functions - Chapter 2 Review - Exercises: 87

Answer

$1+\sqrt{x}$

Work Step by Step

We are given:
$f(x)=\sqrt{1-x}$, $g(x)=1-x^{2}$ and $h(x)=1+\sqrt{x}$
We evaluate:
$(f\circ g\circ h)(x)=f(g(h(x)))=f(g(1+\sqrt{x}))=f(1-(1+\sqrt{x})^{2})=f(1-(1+2\sqrt{x}+x))=f(1-1-2\sqrt{x}-x)=f(-2\sqrt{x}-x)=\sqrt{1-(-2\sqrt{x}-x)}=\sqrt{1+2\sqrt{x}+x}=\sqrt{(1+\sqrt{x})^{2}}=1+\sqrt{x}$